A281813 a(0) = 3, a(n) = 8*n + 4 for n > 0.

3, 12, 20, 28, 36, 44, 52, 60, 68, 76, 84, 92, 100, 108, 116, 124, 132, 140, 148, 156, 164, 172, 180, 188, 196, 204, 212, 220, 228, 236, 244, 252, 260, 268, 276, 284, 292, 300, 308, 316, 324, 332, 340, 348, 356, 364, 372, 380, 388, 396, 404

Offset

0,1

Comments

Consider a 1 X S rectangle on an infinite grid and surround it successively with the minimum number of 1 X 1 tiles: the initial S on step 0, 2S + 6 on step 1, 2S + 14 on step 2, and so on. This sequence is case S = 3. See Ivaturi link for a connection to sieving for primes.

Links

Table of n, a(n) for n=0..50.

Rayan Ivaturi, Ripple Numbers

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

G.f.: (3 + 6*x - x^2)/(1 - x)^2.

a(n) = A017113(n) for n>0, a(0) = 3.

Prog

/*
* This Java program generates the ripple number sequences (first 11 terms)
* for the seed values 1 to 9
*/
/**
* @author Rayan Ivaturi
*/
public class RippleNumbers {
    public static void main(String[] args) {
        int limit = 10;
        for (int seed = 1; seed < limit; seed++) {
            System.out.print("{" + seed);
            int base = 2 * seed + 6;
            System.out.print(", " + base);
            for (int i = 1; i < limit; i++) {
                int ripple = base + 8 * i;
                System.out.print(", " + ripple);
            }
            System.out.println("}");
        }
    }
}
(PARI) a(n)=if(n>0, 8*n+4, 3) \\ Charles R Greathouse IV, Feb 07 2017

Crossrefs

Cf. A017113.

Other 'ripple sequences': A022144 (s=1), A017089 (s=2).

Sequence in context: A257942 A063244 A344015 * A063102 A122576 A212760

Adjacent sequences: A281810 A281811 A281812 * A281814 A281815 A281816

Keyword

nonn,easy,less

Author

Rayan Ivaturi, Jan 30 2017

Extensions

Entry revised by Editors of OEIS, Feb 09 2017

Status

approved